Service life estimation of polymer materials by accelerated aging is an indispensable tool which provides either a qualitative or quantitative comparison depending on the methodology used. In this paper, a new approach of reliably evaluating the service life in relatively short time durations is described. The proposed method is based on the cumulative damage theory incorporating the statistical treatment of data to provide a realistic output which would be useful for designing products.from selected formulations. It is assumed in this methodology that the overall deterioration of a given material is a cumulative effect of individual deteriorating stresses. It can be computed from the experimental data collected for the aging in various stress conditions, wherein no more than two stresses are accelerated at a time. The aging data obtained from a number of accelerated tests can be analysed using the proposed mathematical equations to simulate the life data for the normal service conditions. This approach is also useful in carrying out comparative studies between two materials with respect to overall performance in the given service environment. The comparison can be either direct or indirect depending on the nature of the product and the service environment selected. The proposed method of modified cumulative damage is described in this paper with all the salient features of the method and its mathematical treatment. A comparison of the proposed approach with other existing methodology is presented to highlight the advantages of the new approach. The experimental work validating the proposed approach and its applications will be described in subsequent publications.